Hostname: page-component-669899f699-7tmb6 Total loading time: 0 Render date: 2025-04-26T22:59:31.221Z Has data issue: false hasContentIssue false
  • English
  • Français

Proper efficiency in linear vector maximum problems with nonlinear constraints

Published online by Cambridge University Press:  09 April 2009

T. R. Gulati  and
M. A. Islam
T. R. Gulati
Affiliation:
Department of Mathematics, University of Roorkee, Roorkee 247667, India
M. A. Islam
Affiliation:
Department of Mathematics, University of Dhaka, Dhaka-2, Bangladesh
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A linear vector maximum problem with nonlinear constraints is considered. A condition is derived which is necessary for an efficient solution and sufficient for a properly efficient solution of this problem. This leads to sufficient conditions for an efficient solution to be properly efficient. An example is discussed at the end.

MSC classification

Secondary: 90C31: Sensitivity, stability, parametric optimization 90C30: Nonlinear programming
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 229 - 235
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Benson, H. P. and Morin, T. L., ‘The vector maximization problem: proper efficiency and stability’, SIAM J. Appl. Math. 32 (1977), 64–72.CrossRefGoogle Scholar
[2]Bhatia, D. and Gupta, B., ‘Efficiency in certain nonlinear fractional vector maximization problems’, Indian J. Pure Appl. Math. 11 (1980), 669–672.Google Scholar
[3]Choo, E. U., ‘Proper efficiency and the linear fractional vector maximum problem’, Oper. Res. 32 (1984), 216–220.CrossRefGoogle Scholar
[4]Geoffrion, A. M., ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 618–630.CrossRefGoogle Scholar
[5]Isermann, H., ‘Proper efficiency and the linear vector maximum problem’, Oper. Res. 22 (1974), 189–191.CrossRefGoogle Scholar
[6]Kaul, R. N. and Gupta, B., ‘Efficiency and linear fractional vector maximum problem’, Z. Angew. Math. Mech. 60 (1980), 112–113.CrossRefGoogle Scholar
[7]Kaul, R. N. and Gupta, B., ‘Multi-objective programming in complex space’, Z. Angew Math. Mech 61 (1981), 599–601.CrossRefGoogle Scholar
[8]Klinger, A., ‘Improper solutions of the vector maximum problem’, Oper. Res. 15 (1967), 570–572.CrossRefGoogle Scholar
[9]Kuhn, H. W. and Tucker, A. W., ‘Nonlinear programming’, Proceeding Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492 (Univ. of California Press, Berkeley, California, 1951).Google Scholar
[10]Mangasarian, O. L., Nonlinear programming (McGraw-Hill Inc., New York, 1969).Google Scholar